Sometimes people say that water is removed from clothes in d0 ip6qh ic) fj,(2foea spin dryer by centrifugal force thq cpd i(, e6j2fihf0)orowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels arodz(n ;.gvxuo d56lg0 g sqc.x8und a sharp curve at a constant 60 km/h as when it travels around al vq g0dzg .x56cn(gxsu8o;. d gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly roagm1sxp7fj;s 2d. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) j21gf ms; p7xson a level stretch near the bottom of a hill?

Describe all the forces acting on a child rizfj )o re1/w rl*71xeoding a horse on a merry-go-round. Which of these forces provides the c ojfo/z1r)lrwe7e1 x* entripetal acceleration of the child?

A bucket of water can be whiyh.h-0 yxk4f*nzs i*arled in a vertical circle without the water spilling out, even at the top 4y* hnfzx*k.a-hi sy0 of the circle when the bucket is upside down. Explain.

How many “accelerators” do you mjfs:d d z;bgiv+r 5z25 1jm:thave in your car? There are at least three controls in the car which can be used to cause tm 152id jrtgzs::+;j bmdvfz5he car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shwyy-)o p rvs79own in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s y)ow -vryp7 s9second law.

Why do bicycle riders lea7oymc 0s4 cs+mn inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankisyrsuc pl *+rn8c -,f+ng angle given its speed and radius of the tur8frcs *+uysplcr- ,n+n?

A girl is whirling a ball on a string around her head in a horizontal planf(xd06 dzd 6s0: ) x6karakwnse. She wants to let go at precisely the right time so that the ball will hit a target on the other side or a0k)xn6 sa zw6dd f0:k6sd(xf the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? I-a-vbc+1o o .nrp,knjf so, how large a force? Con-vjo pb+n -1rk.,a consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what watcc r+2vaxq:nip; hm(qc(- g8ys would the Moon’s orbit be different?8ainvqmc:;c c2-(t+ ghr qxp(

Which pulls harder gravitationally, the Earth on the Moyvh,b z 5bdtt+s8;a;con, or the Moon on the Earth? Which acceleratb b;5,av zcydhts;+ t8es more?

The Sun's gravitatio- m3ogyg9l; skypr39 gnal pull on the Earth is much larger than the Moon's. Yet the Moonm-sg9yg yl3;g o 39kpr's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects arsjgjz )eokm( +wr15z97oo( re e at work? Do they oppo gk9ze7w rj5mj1 osoerz)((o+se each other?

The gravitational force on the Moon due to the Eay w mecs9zc70i0 m+t2vrth is only about half the force7c smtwm+e 9c0z0y2iv on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sm-bfds)oxed5 -emb/vh5axki58tx f 23aller than the centripetal acceleration of tmd-b5a83o5 x -f ti d ekh5)2xvsfxbe/he Earth?

Would it require less speed to launch a satelxwuin lfm7jtd 4*85h 5lite (a) toward the east or (b) toward the west? x7h5j*4twiufl58 dn mConsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as,5 el-gd17 / 9k jinm5jxvrhji measured by a scale in a moving elevator: when the elevatorv9 1j7ljirx- jmek5 ,5dhgni/ (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space cot *go aizno7 4,uof0/,ihe6q guld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can th4z 7oieoa0 ,6ufoi/*,hng q tgink of.

Explain how a runner experiences “free fall” or “apparent weigso j93ccgl(g3z pmy)dq0j 1 /shtlessness” betweenc) lqs dj3o1sm3pyg0zc g/j9( steps.

The Earth moves faster ir p,q( ( 3+1oxy*yqzg ;evb.db/sv mwan its orbit around the Sun in January than in July. Is the (3b xev1 .qbdq (g+zv;*sr mypya,/woEarth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known uno)osa zvdwr/v83z 0o ,til it was discovered to have a moon. Explain how this discoveryoo,8zz)3v s0 w oa/drv enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much ljpci.bkfhx0q t s4s wh8m 9( ug(w.5t5arger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the cen(sm tfwu5 894jkb5g w(. q.xhshc0tpiter of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelin 7o(gmhd.jpc3tvmw23g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arouiqu9nf59pq 6q, yo ql9nd the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circ659q lq qi9 qou,9pfynle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N i-y5ixsxgvh(q5 sj2+orm -cw .s exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. h r2 s-vsqj+5.x5x c(wy-omgiCalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km s87pay2ukp w2e s/6cw1b)up6zxpskxl 9 4(rl from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in t9/r2p l(yakx spu61z p2kwbx 67lwscsp )ue84 erms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay p/t9q. 01 aayg21mepxvw z)fgon the edge of a potter’s wheel turning at1.qtpg v19apme yfx0g/2awz ) 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifoq:2l8i dhw+g arm rate in a vertical circle of radius 72.0 cm , ada l:ih g+w28qs shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a tuv (mv6b1 );qcu-qoqvyrn of radius 77 m on a flat road if the coefficient of static friction between tires aq) v;oy 6 cqv(1qmvbu-nd road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tire vg t.m56a8yrvs and the road if a car is to rou.v mya68 rg5vtnd a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed tias 3l0 tz*m)quyd2x 9o rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt bz l2uait* s dm39q0)yxy the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable o /.ajky(ix y.3d6)tdgqffio4lk 6-2 bbtwin4 f variable speed. When the speed of the turntable is sl(-din kyt6ty k qf ii42d4o lg)f/ .jbbax6.w3owly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upskd*dxv6s of7w/ b: l0rbt2l .f0njy*ride down at the top of a circl27y0 *vrdnfbl .*b lt 0o 6fkwsrj:/xde
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top p7lesytq leh( *e(wtl)b89xwd*w 3 -h of a hiewhpw 9bl y)7(qle *3ld-t8t (xw *sehll (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter o:+uzbumuh 53 Ferris wheel need to make for the passengers to feel “weightless” at the topmost po5u:o+muz bh3 uint?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad8n ih2u, pqu. u*lbph6+xr3p xius 1.10 m. At thei3 6q nbp2r.hhx,8u lx+upu*p lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from z, 6vz+/hkf,ek- ,dpeo2gc t jthe axis of rotation is to experi2 ,zhoz jg-/k6e,fdp v, kec+tence an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carn- dp/(m fg pgxcv,2hmc,h5jj0ival, people are rotated in a cylindrically walled "room." (x/p jhh cmv mfp520cg-gd,,j(See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tabl10*:sy k aep a21ityajetop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 51y aaj12ys p iat*:ek0-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ban t9wenip28+kll which revolves on a string 0.600 m long. In particular, find the magnitude of 8 e ptn+i92knw $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked forfgosa n6 d75y8 a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masser s-hkm glr6(;s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at qtu8idq. fw r+d4b * ljqjkk4(.c,pl6 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the 5 )ssy/sb gjn7net force exerted on the car (by the ground) in Example 5-/ ys5)sjg7snb 8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 a r1cmle1sy4pld3kw z.c- (h2yccelerates uniformly from the pit area, going from resl (3z khde2yw 1pcmcy1lrs.4-t to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particxje7:(s7w u g2c/sxe dular instant, its acceleration iscx/uwe7e2d (sx sj g:7 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecrak knm;en9 h44 5. zwarx.wr)dhft 12,800 km (2 Earth radii) above the Earth’s surface if4w5ka4d.r 9)xwem hn;h.zknr its mass is 1350 kg.   

  At the surface of a cero+npv(z,c i4l tain planet, the gravitational acceleration g has a magnitude of 12 m/ +l o4z(nipv,cs$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration dt9bom uaz: vwv*5-3 abd +.gmuue to gravity on the Moon. The Moon's radius is 1.7w.bd+m*vz5a -: 9 omatuuv g3b4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, z /-zlzpy+8f0cz+k(jth uu- :zkki+t but has the same mass. What is the 0zjiuzk:z l +htf(t-c+k/-8zpy+ukzacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thed4+c/y dmtf)y e8 9bk+aedsa( dn.d5 c same radius. What is g near iet )/ (9cd8+ddmak ydyds5nc.fbae4 +ts surface?   

  Two objects attract each other w9g, z+ggm8e7taej p; gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effectivh*lxws/4f5 w1xx0f1 q5lwba ve value of g , the acceleration of gravity, at (a) 3200 m b 4 fv51wwql5lx01f/wxh ax* s   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthc dywcen* 2 px,1* dwvr**cig/ where thegravitational acceleration due to th* dx,r*cg*iwpd/yv nwcc2e* 1 e Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the md*41 sz :kiyvyxypoc )pz r/73ass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.i:3y y kopxv/dcz)714z* prsy    $\times10^12$

  A typical white-dwarf star, which once was5 ;qy zfwfn-a0 an average star like our Sun but is now in the last stage of its evolu -z0; 5faqwfnytion, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronaut5 pyvezy61; ris feel weightless while orbiting in the space shuttle. Your friends respond that they tho;peyzi1vy65 r ught gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calx5w3:vl yat j2culate the magnitude and direction of the total gravitational force exerted on one sphere by the other threetav5l3j: 2 xwy.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets,z zp0ww:;epax)o6 f s line up on the same side of the Sun. Calculate the total force on the Earth due to Venu;)wwzx:epz 6,paof0s s, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface ou9:d56niidu7* f1c aliqgb 6 ef Mars is 0.38 of what it is on E6 :dg9nld 71ebiqi 6ufui*5acarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the rin s5vuo+)w3 +bldc:Earth and its distance from the Sun. [Note: Compdnwi3rcl+u:)vos +b 5 are your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinqorh3taisa.iu q f;iu3s, jk*243j4hg in a stable circular orbit about the Earth at a iuok i j a,434u33rhhfsa2 qj; t*sqi.height of 3600 km.    $\times 10^3$

  The space shuttle release9iotlradgtb5c394q9ja wb: mz*6ua1s a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occu9d4b9mgz5ucw1blqio a a:ta3 j 69*rtrs?    $\times 10^3$

  At what rate must a cylindre n 7/9f bhcycz0j0m.xical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one r.7znx0/fbc cjm9e y0h evolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eaybwi-tve edvt++ 08r ,rth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small comp d- w,+e0iebvyr vtt+8ared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have +qx-0qjmy5/u z-r xcwto be launched from the top of Mt. Everest to be placed in a circu-+ /x c5r0yj-xuqqzwmlar orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orewwr/d(.y :pmbit the Moon at an altitude of about 100 km. How long did it tdp(ry: w./m ewake to go around the Moon once?    s

  The rings of Saturn are composed of chunks p ao6f a aywy272xk48xof ice that orbit the planet. The inner radius of xa 6kfpy2x 8w 2aya47othe rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diamih7- kysi cvh1)ze( *geter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (c *hks) g7 z(ii-vy1heb) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cen,i1dh;8mo1n ls2wcn;n o .hdster of the Earth'1l;w8ocsoi2 ;.d 1h hnn mns,ds Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equam/n)q ye4n +eul mass. They are observed to be separated by 360 million km and take 5.7 Earth years t4/yqmn)u nee+o orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5v8 uh s98zo*mu8r nbh.5-kg woman in an elevator that *u8zvh.oh 98br8mns umoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an eleva:,(sw tpsvgfx 9p/9rhtor. The cord can wi xsts 9/w9(hp:p,g rvfthstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits 1)yxre5px -bxvery near the surface of a planet with period T , the density (m1ep-rx5xx )by ass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of t lf7pm7+*kagh he Moon (27.4 d) to determine the period of an artificial satellite orbiting very near theam*k77hpl+fg Earth’s surface.    s

  The asteroid Icarus, though only a few hun3t3q urh 5*.h,jq/cyu+ qwjhwdred meters across, orbits the Sun like the* q,+w .wch3hqj/u th5j ryq3u planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4pm ka t-y;atmo;sw.i3h1prh,z*17q a.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes verknit/1;k 2qn:2u) fb5rwebd py close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from thep dte rqfki 1bwubnn2)/2k5:; Sun.]    $\times 10^6$

  Our Sun rotates about the cewrj b6:j* hm,fc:p7qwnter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, ak y/6isf i0g;qlq2mh5nd mean distance for the four largest moons of Jupiter (those 20y6kqms; /fglq5hi i discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period a, +eawop 0w 62v0rnnoxnd distance of the Moon. on na 6,pxvoe w0+wr02   $\times 10^{24}$

  Determine the mean distance1au(pp* osz+i4a egv7 from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods+*oaiv71a ueg (ps4 zp given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and kvi tfy(5k+i1i6sqq+ qe0 -leJupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun56q qs0+kvq 1ikefe( -+yliti but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bp.mx h2cb3-qypg,5jbklb tth9 uu 52(and completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, 3q9-y ct(m glup5bhbu 5 h,.kx2j 2bptthis planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a ha ahv*3w a;nfsvjyo ;(d dtm81.nging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? Hiswa(y; .fh1;a8jomnv svt *dd3 mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth / 5-8kqr cajhu,jh-+k f/fmld’s surface will the acceleration of gravity be half what it is on f-fu8/+5 mhqlhca, j/ k- krdjthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands andt c*kns:t o. o+xad7r/ spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kgat:7x /dr.tco n*osk +, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the ap/5)qmryrha0f -*i bm5 fr,7vreo: q bhparent acceleration of gravity at the equator is slightly less than it woub70f5 -*q5 mih ofbr,ry/ qrehv arm:)ld be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft a: gkh4q-4 npgtraveling directly from the Earth to the Moon experience zerog-gq 44kp:ah n net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, butvtjqks:m,ou.dzn5qr* 8: y -b when you stand on a bathroom scale in an elevatorks b,d vnjuz-y r5*t8:q .m:oq, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will r,2u .ytuwk0fwoyy( u )otate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an e.yuftw(yyw 0 )uk2uo,ffect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (F;(r1 .tflrkr e s n9v4tamg/4:myhh c+ig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet ldb8z*a8 kjp7a d)s8v in terms of its radius r, the acceleration due to gravity at its surface and the gravitational codzap8b* 88)ks a jvl7dnstant G.

A plumb bob (a mass m hanging on a string) is deflected waw:.8 )*;vljnh x4 z*pviq xgx0xzz5from the vertical by an a5xx wa0i v) zv:hz 4 qjpgn8wxz.l;**xngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffic)2yq m9lv,j qeient of static friction is 0.30 (wet pavement), at what ran,velj2q)9 mqy ge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at tl;l 9p fvq xtnkg-s6*+he equator 6tx*llq+s g;9 fp -nkvwere apparently weightless?    $\times 10^3$s

  Two equal-mass stars meo*c kca9b( dygj7wcr1(z+ 6jxh *3gy/ 2rhzvaintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constajcxq j.q.*s b2nt speed rounds a curve of radius 235 m. A lamp suspended from the 2*js.qb.j c xqceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massieclh/ea 8 k m(-oob,.xve as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupi eh ekoxlob/ -8c.ma(,ter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extreme1a().,p5vp advifcb / xw:czkd v2 wbi5)s2utly massive core ivbu.wc(v df db5st aak2 5/ c,2)zv1 xppwi:)in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant m bytli5xe/2eu 0bx/1speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where ylbe2/be 0tiuxm51x/ would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Ss)9o wv)u. ssnystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the su)o9n.w sv)sspeed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), s/ . 5kz9e .. uxwei uop0lgtd-pmi2+yafter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros iui -0se.d zixuk2yp/5oplt+ eg9.. mw s roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satelli m kke9j(xl)6tte in need of repair. You are in a circular orbit of the same radiu(ejmk9t )6 xkls as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of o*l rr/oov .bi7mtw f: ,b)8fj3000 years. (a) What is its mean distance from the rv:7jobolm.) * b/t ro,i8ffwSun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could y rilm:+j2w)xs8 pq,ge7 op.ractually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumpie plso xgp+.ry,m:287r) w jqtions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around j,s x:pupr7;f,iyd pvx8q.z e+deo5-the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center o: d.eyvjdrpupspe+85- ,x7qx iz;, f $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squarfz8mcxh0ns (e* 0 .igee 0.50 m on each side. Find the magnitude and dis.i 0fe(h zn8meg0x *crection of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the E+ddjtrbh5 v4s2l 4j1 zarth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long em 4z10/zo atkg.v9lr 1 ;zdjesweep second hand on your wrist . zzld4; ok1jg1/reatv 0 9zemwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weiqz -cc 6wj1jw4;km5 hgght around in a circle below you on a 0.25-m piece of fishing line.g; w45 w-hc1cjj zk6qm The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new h *:9imx jzc 4l u9k;dw4d1jgozighway is designed so that a car travelin;z*x 1dzl4w :mjjgk9i 9 4oucdg at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Ac l6(mlj0 c:fm zs,:cuqela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (qulm ,f::0z(m6cl jscapproximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$